Manual Asymptotic Behavior of Monodromy: Singularly Perturbed Differential Equations on a Riemann Surface

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Solodukhin More by Kirill Krasnov Search this author in:. We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background.

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For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified "tortoise" coordinate.

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The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions.

Topologically, in all cases both surfaces are a sphere with a set of marked points; for BTZ and 4D Schwarzschild black holes there is 3 marked points. In certain limits the surfaces can be characterized very explicitly.


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Asymptotic Behavior of Monodromy : Carlos Simpson :

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Journal of the European Mathematical Society - Author Index

Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold.

Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.